Show an example of a rational number that is between 10−−√ and 11−−√ .

Answer 1

To find a rational number between $\sqrt{10}$ and $\sqrt{11}$, we can write down the decimal approximations and then express those as fractions. We have $\sqrt{10} \approx 3.162$ and $\sqrt{11} \approx 3.317$. Since $\frac{10}{3} = 3.333\ldots$ is larger than $3.162$ and smaller than $3.317$, it lies between $\sqrt{10}$ and $\sqrt{11}$. Thus, a rational number between $\sqrt{10}$ and $\sqrt{11}$ is $\boxed{\frac{10}{3}}$.

Answer 2

Which irrational number is between 14−−√ and 18−−√ ?

Answer 3

To find an irrational number between $\sqrt{14}$ and $\sqrt{18}$, we can try taking the average of these two values. We have $\sqrt{14} \approx 3.742$ and $\sqrt{18} \approx 4.242$. A number that lies between these two values is $\frac{\sqrt{14} + \sqrt{18}}{2}$. However, this expression involves adding irrational numbers, so the resulting value is still irrational.

Therefore, a specific irrational number between $\sqrt{14}$ and $\sqrt{18}$ is $\boxed{3.992}$.

Answer 4

you missed this one, where you need to Show an example of a rational number that is between √10 and √11
You said that 3.162 < 10/3 < 3.317
Clearly that is wrong. So try something like 3.2 = 16/5

Answer 5

Apologies for the mistake in my previous response. You are correct. To provide a rational number between $\sqrt{10}$ and $\sqrt{11}$, we can use the approximation $\sqrt{10} \approx 3.162$ and $\sqrt{11} \approx 3.317$. One rational number that lies between these values is $3.2$, which can be expressed as $\frac{16}{5}$. Therefore, an example of a rational number between $\sqrt{10}$ and $\sqrt{11}$ is $\boxed{\frac{16}{5}}$.